Proving that the matrix is invertible given the eigenvalues?

[theBEAST]

Homework Statement

Given an unknown matrix with eigenvalues 1,2,3, prove that it is invertible?

The Attempt at a Solution

If the det = 0, then there exists an eigenvalue = 0. Since none of the eigenvalues are 0, then the det ≠ 0 and thus the matrix is invertible. Is this a valid proof?

 

[HallsofIvy]

Yes, it is.